we 2 heal it with a resto druid/holy paladin and have a prot warr/prot pally tanks, Make sure ur tanks are fully maxing their dps, they should top out at 110-120k and settle to around 70-80 for overall data (as they do normal dmg when the birds are dead) I use 1 dps trinket for this fight and seem to get my bird down fine but if they are struggling and healing isnt an issue swap in some dps flasks/more dps gear.
Dps help on the birds but the majority of the dmg being done to them has to be the tanks so make sure they are pushing it as hard as they can